class_docstr: edge : b x N x K x C x C semimarkov potentials
code: def _dp_standard(self, edge, lengths=None, force_grad=False):
      semiring = self.semiring
      ssize = semiring.size()
      edge, batch, N, K, C, lengths = self._check_potentials(
          edge, lengths
      )
      edge.requires_grad_(True)
  
      # Init
      # All paths starting at N of len K
      alpha = self._make_chart(1, (batch, N, K, C), edge, force_grad)[0]
  
      # All paths finishing at N with label C
      beta = self._make_chart(N, (batch, C), edge, force_grad)
      beta[0] = semiring.fill(
          beta[0], torch.tensor(True).to(edge.device), semiring.one
      )
  
      # Main.
      for n in range(1, N):
          alpha[:, :, n - 1] = semiring.dot(
              beta[n - 1].view(ssize, batch, 1, 1, C),
              edge[:, :, n - 1].view(ssize, batch, K, C, C),
          )
  
          t = max(n - K, -1)
          f1 = torch.arange(n - 1, t, -1)
          f2 = torch.arange(1, len(f1) + 1)
          beta[n][:] = semiring.sum(
              torch.stack(
                  [alpha[:, :, a, b] for a, b in zip(f1, f2)], dim=-1
              )
          )
      v = semiring.sum(
          torch.stack(
              [beta[l - 1][:, i] for i, l in enumerate(lengths)], dim=1
          )
      )
      return v, [edge], beta
  
file_path: pytorch-struct/torch_struct/semimarkov.py
imports: import torch
  from .helpers import _Struct
label_desc: Use image node_id 3 for calling the SemiMarkov obj's underlying member method code with example usage: obj._dp_standard(edge, lengths, force_grad) and returns: v,  list,  beta